Which of the following ratios is equivalent to 32 ?(1 point)
Responses
96
Start Fraction 9 over 6 End Fraction
1
1
94
Start Fraction 9 over 4 End Fraction
23
Start Fraction 2 over 3 End Fraction
The correct answer is "Start Fraction 9 over 4 End Fraction".
To find a ratio equivalent to 32, we need to divide 32 by a common factor. Let's go through the options:
1. 96: 32 divided by 96 is 1/3, which is not equivalent to 32.
2. Start Fraction 9 over 6 End Fraction: 32 divided by 9/6 is 64/9, which is not equivalent to 32.
3. 1: 32 divided by 1 is 32, which is equivalent to 32.
4. Start Fraction 9 over 4 End Fraction: 32 divided by 9/4 is 128/9, which is not equivalent to 32.
5. Start Fraction 2 over 3 End Fraction: 32 divided by 2/3 is 48, which is not equivalent to 32.
Therefore, the ratio equivalent to 32 is 1.
To determine which of the following ratios is equivalent to 32, let's calculate each ratio and compare them.
Ratio 1: 96
To determine if this ratio is equivalent to 32, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 32. By simplifying, we get:
96 ÷ 32 = 3
Therefore, the simplified ratio is 3, which is not equivalent to 32.
Ratio 2: 9/6
To determine if this ratio is equivalent to 32, we can convert it to a decimal. By dividing 9 by 6, we get:
9 ÷ 6 = 1.5
Therefore, the decimal representation of the ratio is 1.5. Since it is not equal to 32, this ratio is not equivalent.
Ratio 3: 1
Since the ratio is simply 1, it is not equal to 32 and therefore not equivalent.
Ratio 4: 9/4
To determine if this ratio is equivalent to 32, we can once again convert it to a decimal. By dividing 9 by 4, we get:
9 ÷ 4 ≈ 2.25
Therefore, the decimal representation of the ratio is approximately 2.25. Since it is not equal to 32, this ratio is not equivalent.
Ratio 5: 2/3
To determine if this ratio is equivalent to 32, we can convert it to a decimal. By dividing 2 by 3, we get:
2 ÷ 3 ≈ 0.667
Therefore, the decimal representation of the ratio is approximately 0.667. Since it is not equal to 32, this ratio is not equivalent.
From the calculations above, none of the given ratios is equivalent to 32.